The design of irregular planar phased arrays (PAs) characterized by a highly modular architecture is addressed. By exploiting the property of self-replicating tile shapes, also known as rep-tiles, the arising array layouts consist of tiles having different sizes, but equal shapes, all being generated by assembling a finite number of smaller and congruent copies of a single elementary building block. Toward this end, a deterministic optimization strategy is used so that the arising rep-tile arrangement of the planar PA is an optimal tradeoff between complexity, costs, and fitting of user-defined requirements on the radiated power pattern while guaranteeing the complete overlay of the array aperture. As a representative instance, such a synthesis method is applied to tile rectangular apertures with -shaped tromino tiles. A set of representative results is reported for validation purposes but also to point out the possibility/effectiveness of the proposed approach, unlike state-of-the-art tiling techniques, to reliably handle large-size array apertures.